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dim reduction examples Q= > input_dim=
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Max Zwiessele
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3132a0362a
1 changed files with 43 additions and 43 deletions
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@ -14,22 +14,22 @@ default_seed = np.random.seed(123344)
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def BGPLVM(seed=default_seed):
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N = 5
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num_inducing = 4
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Q = 3
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input_dim = 3
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D = 2
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# generate GPLVM-like data
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X = np.random.rand(N, Q)
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lengthscales = np.random.rand(Q)
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k = (GPy.kern.rbf(Q, .5, lengthscales, ARD=True)
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+ GPy.kern.white(Q, 0.01))
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X = np.random.rand(N, input_dim)
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lengthscales = np.random.rand(input_dim)
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k = (GPy.kern.rbf(input_dim, .5, lengthscales, ARD=True)
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+ GPy.kern.white(input_dim, 0.01))
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K = k.K(X)
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Y = np.random.multivariate_normal(np.zeros(N), K, D).T
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lik = Gaussian(Y, normalize=True)
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k = GPy.kern.rbf_inv(Q, .5, np.ones(Q) * 2., ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
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# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
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k = GPy.kern.rbf_inv(input_dim, .5, np.ones(input_dim) * 2., ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
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# k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
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# k = GPy.kern.rbf(input_dim, ARD = False) + GPy.kern.white(input_dim, 0.00001)
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m = GPy.models.BayesianGPLVM(lik, Q, kernel=k, num_inducing=num_inducing)
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m = GPy.models.BayesianGPLVM(lik, input_dim, kernel=k, num_inducing=num_inducing)
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m.lengthscales = lengthscales
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# m.constrain_positive('(rbf|bias|noise|white|S)')
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# m.constrain_fixed('S', 1)
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@ -64,7 +64,7 @@ def GPLVM_oil_100(optimize=True):
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m.plot_latent(labels=m.data_labels)
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return m
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def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
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def sparseGPLVM_oil(optimize=True, N=100, input_dim=6, num_inducing=15, max_iters=50):
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np.random.seed(0)
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data = GPy.util.datasets.oil()
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@ -73,8 +73,8 @@ def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
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Y /= Y.std(0)
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# create simple GP model
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q)
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m = GPy.models.SparseGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing)
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kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim)
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m = GPy.models.SparseGPLVM(Y, input_dim, kernel=kernel, num_inducing=num_inducing)
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m.data_labels = data['Y'].argmax(axis=1)
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# optimize
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@ -86,7 +86,7 @@ def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
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# m.plot_latent(labels=m.data_labels)
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return m
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def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False):
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def swiss_roll(optimize=True, N=1000, num_inducing=15, input_dim=4, sigma=.2, plot=False):
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from GPy.util.datasets import swiss_roll_generated
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from GPy.core.transformations import LogexpClipped
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@ -102,10 +102,10 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
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from sklearn.manifold.isomap import Isomap
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iso = Isomap().fit(Y)
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X = iso.embedding_
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if Q > 2:
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X = np.hstack((X, np.random.randn(N, Q - 2)))
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if input_dim > 2:
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X = np.hstack((X, np.random.randn(N, input_dim - 2)))
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except ImportError:
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X = np.random.randn(N, Q)
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X = np.random.randn(N, input_dim)
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if plot:
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from mpl_toolkits import mplot3d
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@ -121,14 +121,14 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
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var = .5
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S = (var * np.ones_like(X) + np.clip(np.random.randn(N, Q) * var ** 2,
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S = (var * np.ones_like(X) + np.clip(np.random.randn(N, input_dim) * var ** 2,
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- (1 - var),
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(1 - var))) + .001
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Z = np.random.permutation(X)[:num_inducing]
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2)) + GPy.kern.white(input_dim, np.exp(-2))
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m = BayesianGPLVM(Y, Q, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel)
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m = BayesianGPLVM(Y, input_dim, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel)
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m.data_colors = c
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m.data_t = t
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@ -140,19 +140,19 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
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m.optimize('scg', messages=1)
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return m
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def BGPLVM_oil(optimize=True, N=200, Q=7, num_inducing=40, max_iters=1000, plot=False, **k):
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def BGPLVM_oil(optimize=True, N=200, input_dim=7, num_inducing=40, max_iters=1000, plot=False, **k):
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np.random.seed(0)
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data = GPy.util.datasets.oil()
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# create simple GP model
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kernel = GPy.kern.rbf_inv(Q, 1., [.1] * Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2))
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kernel = GPy.kern.rbf_inv(input_dim, 1., [.1] * input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2))
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Y = data['X'][:N]
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Yn = Gaussian(Y, normalize=True)
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# Yn = Y - Y.mean(0)
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# Yn /= Yn.std(0)
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m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, num_inducing=num_inducing, **k)
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m = GPy.models.BayesianGPLVM(Yn, input_dim, kernel=kernel, num_inducing=num_inducing, **k)
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m.data_labels = data['Y'][:N].argmax(axis=1)
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# m.constrain('variance|leng', LogexpClipped())
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@ -193,7 +193,7 @@ def oil_100():
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def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False):
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def _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim=False):
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x = np.linspace(0, 4 * np.pi, N)[:, None]
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s1 = np.vectorize(lambda x: np.sin(x))
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s2 = np.vectorize(lambda x: np.cos(x))
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@ -253,13 +253,13 @@ def bgplvm_simulation_matlab_compare():
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Y = sim_data['Y']
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S = sim_data['S']
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mu = sim_data['mu']
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num_inducing, [_, Q] = 3, mu.shape
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num_inducing, [_, input_dim] = 3, mu.shape
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from GPy.models import mrd
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from GPy import kern
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reload(mrd); reload(kern)
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k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
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m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k,
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k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2))
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m = BayesianGPLVM(Y, input_dim, init="PCA", num_inducing=num_inducing, kernel=k,
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# X=mu,
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# X_variance=S,
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_debug=False)
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@ -273,8 +273,8 @@ def bgplvm_simulation(optimize='scg',
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max_iters=2e4,
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plot_sim=False):
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# from GPy.core.transformations import LogexpClipped
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D1, D2, D3, N, num_inducing, Q = 15, 5, 8, 30, 3, 10
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
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D1, D2, D3, N, num_inducing, input_dim = 15, 5, 8, 30, 3, 10
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim)
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from GPy.models import mrd
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from GPy import kern
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@ -282,8 +282,8 @@ def bgplvm_simulation(optimize='scg',
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Y = Ylist[0]
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k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q)
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m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k)
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k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2)) # + kern.bias(input_dim)
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m = BayesianGPLVM(Y, input_dim, init="PCA", num_inducing=num_inducing, kernel=k)
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# m.constrain('variance|noise', LogexpClipped())
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m['noise'] = Y.var() / 100.
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@ -298,8 +298,8 @@ def bgplvm_simulation(optimize='scg',
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return m
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def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
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D1, D2, D3, N, num_inducing, Q = 60, 20, 36, 60, 6, 5
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
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D1, D2, D3, N, num_inducing, input_dim = 60, 20, 36, 60, 6, 5
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim)
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likelihood_list = [Gaussian(x, normalize=True) for x in Ylist]
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@ -308,8 +308,8 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
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reload(mrd); reload(kern)
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k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
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m = mrd.MRD(likelihood_list, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
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k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2))
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m = mrd.MRD(likelihood_list, input_dim=input_dim, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
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m.ensure_default_constraints()
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for i, bgplvm in enumerate(m.bgplvms):
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@ -330,14 +330,14 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
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def brendan_faces():
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from GPy import kern
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data = GPy.util.datasets.brendan_faces()
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Q = 2
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input_dim = 2
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Y = data['Y'][0:-1:10, :]
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# Y = data['Y']
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Yn = Y - Y.mean()
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Yn /= Yn.std()
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m = GPy.models.GPLVM(Yn, Q)
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# m = GPy.models.BayesianGPLVM(Yn, Q, num_inducing=100)
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m = GPy.models.GPLVM(Yn, input_dim)
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# m = GPy.models.BayesianGPLVM(Yn, input_dim, num_inducing=100)
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# optimize
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m.constrain('rbf|noise|white', GPy.core.transformations.LogexpClipped())
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@ -424,9 +424,9 @@ def robot_wireless():
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def stick_bgplvm(model=None):
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data = GPy.util.datasets.osu_run1()
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Q = 6
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel)
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input_dim = 6
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kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2)) + GPy.kern.white(input_dim, np.exp(-2))
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m = BayesianGPLVM(data['Y'], input_dim, init="PCA", num_inducing=20, kernel=kernel)
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# optimize
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m.ensure_default_constraints()
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m.optimize('scg', messages=1, max_iters=200, xtol=1e-300, ftol=1e-300)
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@ -469,11 +469,11 @@ def cmu_mocap(subject='35', motion=['01'], in_place=True):
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# X -= X.mean(axis=0)
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# X /= X.std(axis=0)
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#
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# Q = 10
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# input_dim = 10
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# num_inducing = 30
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#
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# kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
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# m = GPy.models.BayesianGPLVM(X, Q, kernel=kernel, num_inducing=num_inducing)
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# kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
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# m = GPy.models.BayesianGPLVM(X, input_dim, kernel=kernel, num_inducing=num_inducing)
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# # m.scale_factor = 100.0
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# m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)')
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# from sklearn import cluster
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